Stir together cornmeal, flour, baking powder, sugar and salt in a bowl. In a separate bowl, whisk together eggs, melted butter and milk. Add the wet ingredients to the dry and mix until just combined. Do not overmix.

Remove the pan from the oven and spray with nonstick spray or brush with butter. Scrape the batter into the hot pan and bake for 15-18 minutes, or until lightly golden brown and just baked through.

Let cool in pan for 10 minutes. Remove from pan and let sit out overnight if using for dressing.

Make the dressing:

Preheat oven to 375 degrees F.

Heat the oil in a 9-inch cast iron pan pan over high heat until it begins to shimmer. Add the mushrooms and cook, stirring occasionally, until golden brown and their liquid has evaporated, about 10 minutes. Transfer the mushrooms to a large plate or baking sheet.

Heat butter and oil in large pan over medium high heat. Add the onion, celery and carrots and cook until soft, about 5 minutes. Return the mushrooms to the pan and cook for 1 minute longer.

Transfer the mushroom mixture to a large bowl. Whisk the eggs in a small bowl, then add a bit of hot stock to temper them; set aside. Add the cornbread and 2 cups of the stock to the mushroom mixture and stir to combine. The mixture should be quite wet; if it appears too dry, begin adding the remaining stock, a half cup at a time. Stir in the egg mixture, sage, thyme and parsley and season with salt and pepper to taste.

Scrape the dressing into a large well-seasoned cast iron pan and bake in the oven until firm and the top is golden brown, 25 to 35 minutes.